A method of the initially named kind and also corresponding hollow body elements and component assemblies are for example known in the non-prior published application PCT/EP2005/003893 of Apr. 13, 2005. It is the object of the present invention to so further develop the method of the initially named kind that hollow body elements, in particular rectangular nut elements can be manufactured at favorable prices without having to load the tools that are used such that they fail prematurely. Furthermore the hollow body elements that are manufactured in this way should have excellent mechanical characteristics, for example a high pull-out force, an excellent security against rotation and should moreover show a reduced notch effect, so that the fatigue characteristics of component assemblies comprising a component normally consisting of sheet metal and hollow body elements mounted thereon can be improved also under dynamic loads. Furthermore, the hollow body elements should be capable of being manufactured at an extremely favorable price. Moreover, a particularly advantageous design of a progressive tool used in the manufacture of hollow body elements and also of a rolling mechanism for the purpose of manufacturing hollow body elements should be made available in accordance with the invention.